A conventional two-part rim assembly for tires normally comprises a pair of rim sections having mounting flanges thereof releasably attached together by a plurality of circumferentially disposed bolts. Such a rim assembly is adapted for use on large construction vehicles wherein tire sizes dictate the need therefor. In particular, the two-part rim construction facilitates demounting a tire therefrom by merely releasing the bolts in contrast to other conventional rim assemblies wherein the tire beads must be stretched over one of the rim flanges of a rim assembly. One problem arising with respect to such a two-part rim assembly is one of assuring substantial deflation of the tire prior to detachment of the rim sections from each other.